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Seminars in Systems and Control
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The Centre for Systems Engineering and Applied Mechanics (CESAME) organizes a series of seminars. The seminars are held in the CESAME lecture room, Building EULER, 4-6, av. Georges Lemaître, Louvain-la-Neuve (Parking 13).
For further information, feel free to contact the secretary: 010/47.25.97.
If you wish to receive the seminar announcements by email, please send an email to Nathalie Ponet.
Master students can take this seminar for credit in either of the two
semesters; see INMA2120 for more information.
Look also at the seminars of the departement of mecanics and at the
seminars of the research group on Large Graphs and Networks.
Seminars to come
14/02/2012 (14.00) [Lieu : Bât. Euler]
Samuel MELCHIOR (UCL)
Model reduction of conservation laws
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In continuum mechanics, the unknown fields must satisfy a system of
conservation and constitution laws everywhere in space and time. This can
be reformulated equivalently as weak formulations that can be discretized
using the Finite Element Method (FEM). Usually, the shape and test
functions are piecewise low-order polynomial defined on a compact support.
However, considering totally discrete prolongation and restrictions spaces
can be quite more optimal. This is especially true when the motivation for
using such models is not necessarily to estimate the value of the
quantities everywhere in the domain. For instance, it might be important
to approximate only the relation between several inputs and outputs of the
systems. In this case, the order of the model can be reduced to a much
lower value without losing much accuracy. In this talk, we investigate the
connections between Model Order Reduction (MOR) and multimesh schemes on
Linear Time-Invariant (LTI), Linear Time-Varying (LTV) and nonlinear
dynamical systems.
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21/02/2012 (14.00) [Lieu : Bât. Euler]
Renaud LAMBIOTTE (FUNDP Namur)
TBA
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TBA
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23/02/2012 (16.30) [Lieu : TBA]
Prof. Dr. Michael HINZE (Fachbereich Mathematik, University of Hamburg)
COLLOQUIUM CESAME/MAPA: Mathematics of pde constrained optimization
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| We discuss control problems with PDEs as subsidiary conditions and
take special emphasis on (i) the proper functional analytic setting,
(ii) tailored discrete concepts in the presence of additional
pointwise constraints, and on
(iii) structure exploiting solution algorithms.
The theoretical results are supported by numerical experiments. |
28/02/2012 (14.00) [Lieu : Bât. Euler]
Michel GEVERS (UCL)
Optimal experiment design for open and closed loop identification
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Optimal experiment design for system identification was a
very active research topic in the 1970's: the results at that time
focused on the minimization of different measures of the parameter
covariance matrix. The research on this topic disappeared for more
than a decade. In the mid eighties new results became available that
focused on quality criteria that took account of the objective for
which the model was estimated. These results were based on approximate
variance formulae for the estimated transfer functions, under the
assumption that the model order goes to infinity. Experiment design
experienced a sudden revival of activity from around 2003 under a
triple influence: the advent of new expressions for the variance of
estimated quantities that did not require an assumption of model order
going to infinity, the introduction of the concept of "least costly
identification design", and the development of new optimal design
techniques for identification that convert the optimization problem
into semi-definite programs that can be solved using Linear Matrix
Inequalities. In this talk we shall first review the development of
optimal experiment design. We shall then present new results that
allow one to solve the optimal closed loop experiment design problem,
where the optimization is performed jointly with respect to the
controller and the spectrum of the external excitation. Our results
are based on the partial positive definite matrix completion theorem.
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06/03/2012 (14.00) [Lieu : Bât. Euler]
Manuel LOPEZ-MARTINEZ (Universidad de Sevilla)
Constructive Feedback Linearization Of Mechanical Systems With Friction and Underactuation Degree One
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In this talk we present a constructive methodology to
control a class of unstable underactuated mechanical systems
with underactuation degree one, by means of classical feedback
linearization and Lyapunov design. The design is presented
proposing a dummy output that allows to solve the problem in a constructive way.
We prove that the proposed output solves the problem obtaining
an explicit and compact control law.
The stability result of the obtained solution does
not change when taking into account the friction effects even in the
unactuated coordinate. The new result is applied to obtain a
(almost) global stabilizing scheme for the VTOL aircraft model
with strong input coupling.
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13/03/2012 (14.00) [Lieu : Bât. Euler]
François WIELANT (UCL)
Production d¿un couple étalon adapté à une balance gravitationnelle réalisée à l¿Observatoire Royal de Belgique
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Le laboratoire d¿instrumentation géodynamique de
l¿Observatoire Royal de Belgique a développé un instrument à partir
d¿un Pendule Vertical Symétrique (Symmetrical Vertical Pendulum, SVP),
dont le but est d¿établir une nouvelle mesure de la constante G. Ce
pendule est utilisé comme balance de couples, introduits par le champ
de pesanteur terrestre local g, ainsi que par un actionneur
gravitationnel (paire de masses attractives en mouvement). La
rotation (dans le champ de pesanteur terrestre) des aiguilles d¿une
montre à Quartz fixée sur le bras pendulaire est utilisée pour
produire un couple de comparaison périodique d¿amplitude
constante. Cette présentation traite de la conception d¿un dispositif
de calibration en vue de pouvoir étalonner le couple généré par les
aiguilles de la montre, au sein d¿un instrument pendulaire spécifique
(fixer le rapport d¿échelle entre les amplitudes des deux couples). Ce
dispositif de calibration est constitué d¿un moteur DC miniaturisé,
effectuant une translation dans le champ de pesanteur d¿un corps de
masse connue avec grande précision (micro masse). La maîtrise du
déplacement du corps de masse connue, au sein de l¿instrument
pendulaire, procure la précision attendue d¿un système
d¿étalonnage. La qualité de l¿étalonnage proposée réside dans la
maitrise du déplacement de la micro masse conduisant à un couple
étalon de l¿ordre de 10-7 Nm.
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20/03/2012 (14.00) [Lieu : Bât. Euler]
Vincent TRAAG (UCL)
TBA
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TBA
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17/04/2012 (14.00) [Lieu : Bât. Euler]
Jérémy DEHAYE (FUNDP Namur)
LQ-optimal control of infinite dimensional linear systems with boundary control and observation
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Distributed parameter systems based on partial differential equations can be used to describe the behaviour of many physical setups, e.g. convection-diffusion-reaction systems with a linear or linearized reaction rate and inputs and sensors located on the spatial boundary. These systems can generally be written as abstract infinite-dimensional linear differential systems with boundary control and observation, and the associated operators are thus unbounded.
Under these conditions, difficulties can arise when trying to solve some specific control problems, including the linear-quadratic optimal control problem and the design of the associated stabilizing state feedback. In particular, the method of spectral factorization by symmetric extraction provides an alternative to the resolution of the operator Riccati equation for the LQ-optimal control problem but its convergence relies on the fact that the control and observation operators are bounded.
In order to solve this problem, we consider, under appropriate conditions on the initial equations, a change of variables and an extended abstract linear differential system with bounded control and observation operators. An adapted cost functional can be associated with this extended system and can be interpreted in the framework of the initial one. Solving the LQ-optimal control problem for this cost functional provides a stabilizing feedback at the cost of an approximation in the measurement of the output and the feedback not being the optimal one in general.
As an application, we try to solve the LQ-optimal control problem for a convection-diffusion-reaction system with both distributed and boundary control, and boundary observation. The involved differential operator belongs to the class of Sturm-Liouville operators that are densely defined in the Lebesgue space of square-integrable functions. These systems are used in the modelling of e.g. biochemical processes, such as nonisothermal tubular reactors with axial dispersion, biochemical reactors, UV disinfection and many others.
The main tools of functional analysis used in this framework are the
theories of C_0-semigroups and Riesz-spectral systems, playing a
central role when Sturm-Liouville systems are involved.
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24/04/2012 (14.00) [Lieu : Bât. Euler]
Jaime MORENO (Universidad Nacional Autónoma de México)
Discontinuous Observers with strong convergence properties and some applications
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Despite of the fact that the (global and instantaneous) observability
property implies that the state of a system can be recovered in an
arbitrarily small time (for every state), smooth observers are able to
provide an estimation of the states that converges only asymptotically and
that it is only practically convergent in the presence of uncertainties or
persistent perturbations.
In order to achieve the desired properties of convergence in finite time,
robustness against persistent perturbations and convergence time
independent of the initial conditions, it is necessary to provide the
observer with strong nonlinearities, i.e. discontinuities and not globally
Lipschitz nonlinearities. In the talk some recent developments in this
direction will be presented and the results will be illustrated by means
of some applications.
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08/05/2012 (14.00) [Lieu : Bât. Euler]
Benoit DELHAYE (UCL)
TBA
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TBA
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15/05/2012 (14.00) [Lieu : Bât. Euler]
Holger VOOS (University of Luxembourg)
Development of safe autonomous systems: a perspective
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In the near future, systems with a high degree of autonomy like mobile service robots are expected to provide services in many area of life. They have to execute demanding and complex tasks in a dynamic unstructured environment, collaborate with human users in a natural and intuitive way and adapt themselves to varying conditions. While much effort in research is spent on the investigation and realization of artificial intelligence and autonomy, it is often neglected that a higher degree of autonomy also results in higher safety requirements, especially if these autonomous systems have to interact closely with human users.
This presentation focuses on a perspective for the development of safe autonomous systems. While processes and measures for the design of safety-critical technical systems in general exist, both the structural and behavioral complexity of an autonomous system requires measures to ensure safety that are far beyond the currently existing approaches. However, the application of methods like simulation, testing or formal verification during design time turned out to be rather difficult for the development of safe autonomous systems. Therefore this presentation also considers a supervisory approach where safe autonomous behavior of a system should be achieved via online risk assessment and risk-sensitive action planning and generation.
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Previous seminars
07/02/2012 (14.00) [Lieu : Bât. Euler]
Raf VANDEBRIL (K.U.Leuven)
A centuries-old problem: how to compute the roots of a polynomial
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Asking a pure mathematician how he would determine the eigenvalues of a matrix, odds are
fifty-fifty he'll just reply: ``retrieve them as roots from the characteristic
polynomial''. Confronting a computer scientist with the problem of computing roots of a
polynomial he'll likely answer: ``put the polynomial in a matrix and then compute the
eigenvalues of that matrix''. A confrontation could end in an absurd chicken-and-egg discussion.
Theoretically, the mathematician's idea is as valuable as
the computer scientist's. From a computational point of view, however, it is too time
consuming to compute the characteristic polynomial, and moreover, numerically it is no
good idea either.
Computing eigenvalues is done nowadays with one of the top 10 algorithms of the 20th
century: the QR-algorithm [B.A. Cipra, Siam News 33, 2000]. Root solving is done, in practice, by placing the polynomial
coefficients in a matrix, the so-called companion matrix. The roots are then retrieved by
simply applying the QR-algorithm on the companion matrix; all eigenvalues pop up one after
the other until eventually all eigenvalues/roots are found. Cleve Moler, pointed out,
however, in the Mathworks Newsletter in 1991 that this approach may not yet be optimal: `` it uses n^2
storage and order n^3 time. An algorithm designed specifically for polynomial roots might
use order n storage and n^2 time. ''
The goal of this talk is to elaborate on contemporary root solvers effectively using n
storage and achieving a computational complexity of n^2 operations. Roughly a
decade ago it emerged from exploiting rank structures in matrices, that the companion
matrix exhibited quite some useful, so far unexploited, properties. By splitting the
matrix in two parts a whole variety of algorithms was developed. About the same time that
the first successful fast solvers were developed, Fiedler proved that the companion matrix
is just an instance of a whole family of matrices, suitable for computing roots of a
polynomial. We will show that one can also, cheaply, and fastly compute eigenvalues based
on such Fiedler factorizations of companion matrices. The algorithm is simple in nature and numerical
evidence shows that this approach supersedes --in terms of speed-- the fastest currently
available root solvers.
This is joint work with
David Watkins and Jared Aurentz
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31/01/2012 (14.00) [Lieu : Bât. Euler]
Daniel ALAZARD (Supaero Toulouse)
Control design and reverse engineering using observer-based
structures: Application to the control of flexible aerospace vehicles (slides)
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This seminar aims to present convenient tools, based on the observer-based realization
of a given arbitrary controller, to solve robust, multi-objective and gain-scheduling con-
trol problems. These tools are applied on practical examples in the field of aerospace
engineering (launcher, aircraft flight control, ...).
Observer based compensators are useful for different practical
reasons. The key advantage of these controller structures no doubt
lies in the fact that the controller states are meaningful variables
as estimates of the physical plant states: thus, the interpolation of
controllers or the initialization of switched controllers becomes
easier using observer based realization.
Based on the observer based realization of a given controller, the
Cross Standard Form (CSF) is also introduced as a reverse engineering
tool: i.e. a solution to the generalized inverse optimal control
problem. The CSF is a canonical augmented standard plant whose H_\infty or
H2 optimal controller is a given controller. From the multi-objective
point of view, the general idea is to apply the CSF to a first
controller satisfying nominal performances in order to initialize an
H_\infty design procedure to handle frequency-domain constraints or
robustness specifications.
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24/01/2012 (14.00) [Lieu : Bât. Euler]
Kim McAuley (Department of Chemical Engineering, Queen's University, Canada)
Statistical Methods for Developing Reliable Fundamental Models
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| Fundamental models are used to design, debottleneck, optimize and control chemical processes. Obtaining reliable model predictions requires an appropriate balance between simplicity and complexity of model equations, as well as appropriate values for model parameters. This talk will focus on statistical tools that can assist modellers when they develop model equations, estimate parameters and select conditions for new experiments. One common problem that arises when modeling chemical processes is the large number of parameters that appear in equations describing rates of chemical reactions and transport of species between phases. A modeller with a large and informative data set will be able to reliably estimate a large number of model parameters. When there is insufficient information in the data to reliably estimate all of the model parameters, only a subset of the parameters should be estimated. This talk will introduce easy-to-use parameter ranking and selection techniques (based on mean-squared error) that can help modellers to decide which parameters to estimate to get the best possible model predictions. Use of models to select operating conditions for new dynamic and steady-state experiments will also be discussed. These methods will be illustrated using models and data from a steam-methane reformer, bioreactors, and industrial polymerization processes.
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20/12/2011 (14.00) [Lieu : Bât. Euler]
Wei Dai (Imperial College London)
A Geometric Approach for Sparse Signal Processing: Algorithms
and Performance Guarantees
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| Sparse signal processing is a technology for acquiring and
analyzing sparse signals efficiently. Many signals, including
biomedical signals, sensor network measurements, and social network
data are sparse in the sense that the signal can be well approximated
by only a small number of linear principal components. Sparse signal
processing allows us to work on the intrinsic information directly
without worrying about the details of the signal, hence results in a
large saving in data collection or a huge improvement on data
analysis.
In this talk we discuss a geometric view of sparse signal
processing. More specifically, we look at low-rank matrix completion
and dictionary learning problems in sparse signal processing, show how
these topics can be formulated as optimization problems on Grassmann
manifolds, and discuss what kind of performance guarantees can be
obtained based on the geometric approach. Various applications of
sparse signal processing are also briefly discussed.
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13/12/2011 (14.00) [Lieu : Bât. Euler]
Thibault GIARD (UCL)
Adaptive control of grip force to compensate for static and dynamic torques during object manipulation
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Manipulating a cup by the handle requires compensating for the torque
induced by the moment of the mass of the cup relative to the location
of the handle. In the present study, we investigated the control
strategy of subjects asked to perform grip-lift movements with an
object with center of mass located away from the grip
axis. Participants were asked to lift the manipulandum with a
two-fingers precision grip and stabilize it in front of a visual
target. Subjects showed a gradual and slow adaptation of the grip
force scaling across trials: the grip force tended to decrease slowly
and the temporal coordination between grip force and load torque rates
displayed gradually better-coordinated patterns. Importantly, this
adaptation was much slower than the stabilization of the same
parameters measured either when no torque came into play or after
previous adaptation to the presence of a torque. In contrast, the
maximum rotation induced by the torque was efficiently controlled
after only few trials, and an unexpected decrease in the tangential
torque produced significant overcompensation. An unexpected increase
in torque produced a consistent opposite effect. This shows that the
compensation for the dynamic torque was based on an anticipatory
dynamic counter-torque produced by the arm and wrist motor
commands. The comparatively slow stabilization of grip force control
suggests a specific adaptation process engaged by the presence of the
torque. This paradigm including tangential torques clearly constitutes
a powerful tool to extract the adaptive component of grip control
during object manipulation.
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06/12/2011 (14.00) [Lieu : Bât. Euler]
Alessandro D'INNOCENZO (University of L'Aquila)
Modeling, analysis and design of multi-hop control networks
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A multi-hop Control Network (MCN) consists of a plant where the
communication between sensors, actuators and computational units is
supported by a (wireless) multi-hop communication network, and data
flow is performed using scheduling and routing of sensing and
actuation data. We propose a mathematical framework for modeling and
analyzing systems consisting of multiple control loops closed over a
multi-hop (wireless) communication network. We separate control,
topology, routing, and scheduling and propose formal syntax and
semantics for the dynamics of the composed system, providing an
explicit translation of multi-hop control networks to switched
systems. We propose formal models for analyzing robustness of
multi-hop control networks, where data is exchanged through a
multi-hop communication network subject to disruptions. When
communication disruptions are long, compared to the speed of the
control system, we propose to model them as permanent link
failures. We show that the complexity of analyzing such failures is
NP-hard, and discuss a way to overcome this limitation for practical
cases using compositional analysis. For typical packet transmission
errors, we propose a transient error model where links fail for one
time slot independently of the past and of other links. We provide
sufficient conditions for almost sure stability in presence of
transient link failures, and give efficient decision procedures. We
deal with errors that have random time span and show that, under some
conditions, the permanent failure model can be used as a reliable
abstraction. Our approach is compositional, namely it addresses the
problem of designing scalable scheduling and routing policies for
multiple control loops closed on the same multi-hop control
network. We describe how the translation of multi-hop control networks
to switched systems can be automated, and use it to solve control and
networking co-design challenges in some representative examples, and
to propose a scheduling solution in a mineral floatation control
problem that can be implemented on a time triggered communication
protocols for wireless networks. We address the control design problem
on a MCN that is subject to link failures, where the plant is a SISO
LTI system. We first characterize controllability and observability of
a MCN, by means of necessary and sufficient conditions on the plant
dynamics and on the communication scheduling and routing. We provide a
methodology to design scheduling and routing, in order to satisfy
controllability and observability of a MCN for any link failure that
preserves connectivity of the radio connectivity graph. Then, we
characterize the problem of detecting the failure of links of the
radio connectivity graph: we provide necessary and sufficient
conditions on the plant dynamics and on the communication protocol,
and we provide a methodology to design the network topology,
scheduling and routing to satisfy the above conditions.
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22/11/2011 (14.00) [Lieu : Bât. Euler]
Brian D O ANDERSON (Australian
National University)
Morse Theory and Formation Control
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| Formation shape control for a collection of point agents is concerned
with devising decentralized control laws which will ensure that the
formation will move so that certain inter-agent distances assume
prescribed values. A number of algorithms based on steepest descent of
an error function have been suggested for various problems, and all
display the existence of incorrect equilibria, though often the
equilibria are saddle points or unstable. This talk introduces Morse
theory as a tool for analyzing the number of such equilibria.
Initially a simpler problem is reviewed: that of navigating a point
agent using a steepest descent law to a point in a closed
two-dimensional region containing obstacles. A key conclusion is that
for both the navigation problem and for the formation shape control
problem, there will always be incorrect equilibria associated with any
steepest descent law.
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15/11/2011 (14.00) [Lieu : Bât. Euler]
Vincent BLONDEL (UCL)
Should Belgium be split? A perspective from complex networks, mobile phone data and privacy
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| Many complex networks have their nodes distributed in space. In this talk, we describe some recent results on spatially distributed networks. In particular, we describe results obtained from a community detection method on a large network constructed from communications between millions of mobile phone users. We quantify in this network the decrease with distance of connection probability between mobile phone users and we describe a conjecture about a possible explanation for the observed decrease. Related to this observation, we will also analyse a surprising connection between how people relocate in the US and the eigenvectors of a large matrix. Finally, we will conclude our talk with comments on privacy issues in data collection in large social networks. |
08/11/2011 (14.00) [Lieu : Bât. Euler]
Alexandre MAUROY (Université de Liège)
Dichotomic collective behaviors in networks of pulse-coupled oscillators
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| The study of networks of pulse-coupled firing oscillators is a general and simple paradigm to investigate a wealth of natural phenomena (brain neurons, earthquakes, animal behaviors, etc.). In this framework, the oscillators of the network interact through an instantaneous impulsive coupling: whenever an oscillator fires, it sends out a pulse which instantaneously increments the state of the other oscillators by a constant value.
It is a remarkable fact that networks of pulse-coupled oscillators usually exhibit a dichotomic behavior: either the oscillators achieve perfect synchrony or they converge toward an anti-synchronized configuration. Interestingly, theoretical results confirm the dichotomic behavior for a large class of oscillators, but also suggest that the dichotomic behavior is not a general feature of every network of pulse-coupled oscillators.
In this talk, I will present stability results, both for finite and infinite populations of pulse-coupled oscillators, as well as several related open problems.
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25/10/2011 (14.00) [Lieu : Bât. Euler]
Moussa BALDE (UCAD Dakar)
Stability of Linear Switched Systems
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The talk is about asymptotic stability properties of linear switched
systems.
For the planar linear switched system d/dt x(t) = u(t) A_1
x(t)+(1-u(t)) A_2 x(t), where the real matrices A_1, A_2 in R^{2×2} are
Hurwitz and u(·) : [0, infty[ --> {0, 1} is a measurable function, we
give a coordinate-invariant necessary and sufficient condition on
A_1 and A_2 under which the system is asymptotically stable for
arbitrary switching functions u(.). This condition is mainly given
in terms of the polar form of the determinant map Gamma(A_1,A_2) = 1/2
(tr(A_1)tr(A_2) - tr(A_1 A_2)).
Then under the hypothesis that p subsystems in R^d share a non strict
quadratic Lyapunov function, we provide a large class of switching
signals for which a large class of switched systems are asymptotically
stable. For this purpose we define what we call non chaotic inputs,
which generalize the different notions of inputs with dwell time.
Keywords: Switched systems; Asymptotic stability; Quadratic Lyapunov
functions; Chaotic signals; Omega-limit sets.
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18/10/2011 (14.00) [Lieu : Bât. Euler]
Laurent JACQUES (UCL)
Robust 1-Bit Compressive Sensing: How the Sign of Random Projections Distinguishes Sparse Vectors
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| The Compressive Sensing (CS) framework aims to ease the
burden on analog-to-digital converters (ADCs) by reducing the sampling
rate required to acquire and stably recover sparse signals. Practical
ADCs not only sample but also quantize each measurement to a finite
number of bits; moreover, there is an inverse relationship between the
achievable sampling rate and the bit depth.
In this talk, an alternative CS approach that shifts the emphasis from
the sampling rate to the number of bits per measurement is presented. In
particular, we explore the extreme case of 1-bit CS measurements,
which capture just their sign.
Our results come in two flavors. First, we consider ideal reconstruction from noiseless 1-bit measurements and
provide a lower bound on the best achievable reconstruction error. We
also demonstrate that a large class of measurement mappings achieve
this optimal bound.
Second, we consider reconstruction robustness to
measurement errors and noise and introduce the Binary
{\epsilon}-Stable Embedding (B{\epsilon}SE) property, which
characterizes the robustness measurement process to sign changes.
We show the same class of matrices that provide optimal noiseless
performance also enable such a robust mapping.
On the practical side, we introduce the Binary Iterative Hard Thresholding (BIHT) algorithm
for signal reconstruction from 1-bit measurements that offers state-of-the-art performance.
Joint work with J. Laska (Rice Univ., USA), P. Boufounos (MERL, USA)
and R. Baraniuk (Rice Univ., USA)
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11/10/2011 (14.00) [Lieu : Bât. Euler]
François-Xavier ORBAN DE XIVRY (UCL)
Nearest Stable System
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| Stability is a crucial property in the study of dynamical
systems. We focus on the problem of enforcing the stability of a
system a posteriori. The system can be a matrix or a polynomial either
in continuous-time or in discrete-time. We present an algorithm that
constructs a sequence of successive stable iterates that tend to a
nearest stable approximation of a given unstable system. This kind of
algorithm can be useful in identification where the measured system is
stable but the identified model of the system appears to be unstable
due to some factors. |
04/10/2011 (14.00) [Lieu : Bât. Euler]
Patrick DE LEENHEER (University
of Florida)
Optimal placement of Marine Protected Areas
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| Overfishing can lead to the reduction or elimination of fish populations and the degradation or even destruction of their habitats.
This can be prevented by introducing Marine Protected Areas (MPA's), regions in the ocean or along coastlines where fishing is prohibited. MPA's can also lead to larger fish densities outside the protected area through spill-over,
which in turn may increase the fishing yield. A natural question in this context, is where exactly to establish
an MPA, in order to maximize these benefits. We address this problem along a one-dimensional stretch of coast-line, by first proposing a model for the fish dynamics. Fish are assumed to move diffusively, and are subject to recruitment, natural death and harvesting through fishing. Our problem is then cast as an optimal control problem
for the steady state equation corresponding to the PDE which models the fish dynamics. The cost index being maximized is a weighted sum of the average fish density and the average fishing yield. We show that optimal controls exist, and will see that the form of an optimal control -and hence the location of the MPA- is determined by two key model parameters, namely the length of the coastline, and the weight of the average fish density appearing in the cost index. If these parameters are large enough -and precisely how large, can be calculated exactly- our results indicate when and where an MPA should be established.
The main mathematical tool used to prove our results is Pontryagin's maximum principle.
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20/09/2011 (14.00) [Lieu : Bât. Euler]
Gilles MEYER (Université de Liège)
Linear regression on fixed-rank matrices: a Riemannian approach (slides)
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| In this work, we address the problem of learning a linear regression
model parameterized by a fixed-rank matrix. We deal with the case of
fixed-rank symmetric positive semidefinite matrices and the case of
fixed-rank non-symmetric matrices. The focus is on the nonlinear
nature of the search space and on scalability to high-dimensional
problems. The mathematical developments rely on the theory of batch
and online gradient descent algorithms adapted to the Riemannian
geometry that underlies the set of fixed-rank matrices. The resulting
algorithms scale to high-dimensional problems, enjoy local convergence
properties, favorably compete with the state-of-the-art and confer a
geometric basis to recent contributions on learning fixed-rank
matrices. The considered linear regression framework encompasses many
modern machine learning applications including the learning of a
low-rank distance, low-rank matrix completion, learning on data pairs,
ranking or multi-task learning. |
24/05/2011 (15.00) [Lieu : Bât. Euler]
Cécile PIRET (UCL)
Solving Partial Differential Equations on Arbitrary Surfaces using the Radial Basis Functions Method
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| The Radial Basis Functions (RBFs) method was introduced in the 1970s as an interpolation technique and was adapted in the 1990s to solve partial differential equations (PDEs). Although it is a fairly new technique, its advantages (amongst others, it is meshless, spectrally accurate and works in N dimensions) have made it a powerful tool to accurately and stably discretize differential operators, and thus solve PDEs on quite complex geometries. In this talk, a brief outline of the method will be given and a novel technique to solve PDEs on arbitrary surfaces via RBFs will be presented. |
10/05/2011 (15.00) [Lieu : Bât. Euler]
Dimos DIMAROGONAS (KTH)
Bridging the gap between multi-agent navigation and networked control
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| The development of decentralized control methodologies for navigation of multi-robot/vehicle systems is of paramount importance for the
faster convergence and overall deployment of such systems in various applications including formation control, search and rescue missions, manufacturing,
multi-UAV/UGV operations and many more. On the other hand, it is important to consider network and limited communication aspects between the agents
when designing such controllers. While a lot of research has been devoted to both aspects of multi-agent control, there is still shortage in the
unification of navigation and networked specs. In this talk I will present parts of our research within the two areas and propose possible future
research directions towards unification. |
3/05/2011 (15.00) [Lieu : Bât. Euler]
John LATAIRE (VUB)
A frequency domain approach to the identification of time-varying systems
|
| A time-varying system is a system whose dynamic behaviour changes with time.
As an example consider a swinging mass, attached to a rod with a varying length. As this rod shortens, the speed of oscillation increases,
yielding a time-varying resonance frequency. Most existing identification tools for time-varying systems have been formulated in the time domain.
The present research investigates how a frequency domain formulation could be beneficial for the identification of LTV (Linear Time-Varying) systems.
It turns out that, when using multisine excitations, a lot of insight on the evolution of the instantaneous dynamics can be extracted from a
simple inspection of the spectral response of the system. This will be elucidated during the presentation |
26/04/2011 (15.00) [Lieu : Bât. Euler]
Arnaud BROWET (UCL)
A new algorithm to compute communities in large networks:
application to image and video processing
|
| During the last years, there has been an increasing interest for large
graph analysis due to the development of network modeling in various
areas. Real networks have an high tendency to cluster themselves in
community structures, i.e. in groups of highly connected vertices with
weak links between groups. The Louvain method is a community detection
algorithm that has proven its high capacity to extract good
communities. In this talk, we will present a new community detection
technique based on a fast approximation of the classical Louvain
method with only one assignment and one correction step. We will show
that, in spite of its simplicity, the method also extracts good
community structures and can even be better in terms of quality than
the classical Louvain method when the uncertainty of the graph is
increasing. We will apply this algorithm to the image segmentation and
video tracking problems. |
07/04/2011 (16.30) [Lieu : Bât. Euler]
Augusto PONCE (UCL)
COLLOQUIUM CESAME/MAPA: Peut-on détecter les singularités des cristaux liquides ?
|
| Un problème de minimisation issu d'un modèle de cristaux liquides met en
évidence la question du bon choix de la classe de fonctions admissibles
que nous rencontrons souvent en calcul de variations. Puisque ces
fonctions doivent être à valeurs dans la sphère, des obstacles
topologiques jouent aussi un rôle dans ce problème. Nous nous
intéressons en particulier à savoir comment détecter les singularités
topologiques et comment les distinguer des singularités analytiques. |
5/04/2011 (15.00) [Lieu : Bât. Euler]
Paolo FRASCA (Politecnico di Torino)
Graph coverings and gossip coverage control
|
| Problems of unsupervised deployment of robotic networks and optimal partitioning of large complex environments are important
in engineering applications and open up interesting theoretical challenges. Classical techniques, based on Voronoi partitions, rely on two
assumptions: the environment to apportion is convex, and communication is synchronous and reliable along the edges of the Delaunay graph
induced by the robots' positions. In this talk I will present a novel solution which allows the robots to optimally deploy in non-convex
environments by using unreliable gossip communication. Joint work with R. Carli (University of Padova), J. W. Durham and F. Bullo (UCSB) |
29/03/2011 (15.00) [Lieu : Bât. Euler]
Jean-Pierre TIGNOL (UCL)
A chain property for cube-scalar matrices of order 3
|
| Matrices a of order 3 such that a3 is a scalar matrix are the vertices of a directed graph in which an edge goes from a to b
when aba^{-1}b^{-1}= e^{2i\pi/3}. This talk will present a proof that any two cube-scalar matrices can be connected by a path of length at
most 4, using some exceptional algebraic structures. |
22/03/2011 (15.00) [Lieu : Bât. Euler]
Jean-Jacques ORBAN DE XIVRY (UCL)
Temporal Discounting of Reward and the Cost of Time in Motor Control
|
| Why do movements take a characteristic amount of time, and why do diseases that affect the reward system alter control of movements?
Suppose that the purpose of any movement is to position our body in a more rewarding state. People and other animals discount future reward as a
hyperbolic function of time. In this presentation, I'll show that, across populations of people and monkeys, there is a correlation between discounting
of reward and control of movements. I'll consider saccadic eye movements and hypothesize that duration of a movement is equivalent to a delay of reward.
The hyperbolic cost of this delay not only accounts for kinematics of saccades in adults, it also accounts for the faster saccades of children,
who temporally discount reward more steeply. Our theory explains why saccade velocities increase when reward is elevated, and why disorders in the
encoding of reward, for example in Parkinson's disease and schizophrenia, produce changes in saccade. In addition, delay of reward elevates the cost
of saccades, reducing velocities. Finally, I'll consider coordinated movements that include motion of eyes and head and find that their kinematics is
also consistent with a hyperbolic, reward-dependent cost of time. Therefore, each voluntary movement carries a cost because its duration delays
acquisition of reward. The cost depends on the value that the brain assigns to stimuli, and the rate at which it discounts this value in time.
The motor commands that move our eyes reflect this cost of time. |
8/03/2011 (15.00) [Lieu : Bât. Euler]
Jean-Charles DELVENNE (UCL)
Democracy in Markov Chains and Its Preservation under Local Perturbations (slides)
|
| A sequence of irreducible Markov chains with increasing state
cardinality is called democratic if the sequence of corresponding
invariant probabilities converges to 0 uniformly. Democracy is a
relevant property which naturally shows up when we deal with distributed
algorithms like consensus or with opinion dynamic models: it says that
each agent measure/opinion is going to play a negligeable role in the
asymptotic behavior of the global system. Simple random walks on
undirected graphs of bounded degree and increasing cardinality are one
of the simplest examples of democratic chains. Similar examples can be
built considering more general time-reversible chains. In this paper we
prove a general result which says that, under some technical
assumptions, perturbing the transition probabilities from a finite
number of vertices of a time-reversible democratic sequence of chains,
democracy is preserved. We want to stress the fact that the local
perturbation in general breaks the time-reversibility of the chains. The
main technical assumption needed in our result is the irreducibility of
the limit Markov chains and we show with an example that this assumption
is indeed necessary. |
1/03/2011 (15.00) [Lieu : Bât. Euler]
Claudia ANGELINI (Istituto per le Applicazioni del Calcolo "Mauro Picone", CNR)
Analyzing the Whole Transcriptome by RNA-Seq data: Statistical and Computational Challenges (slides)
|
| The main goal of the whole transcriptome analyses is to identify, characterize and catalogue all the transcripts expressed within a
specific cell/tissue - at a particular stage - with the great potential to determine the correct splicing patterns and the precise structure of genes,
and to quantify the differential expression of transcripts in both physiological and pathological conditions. Until 2004, hybridization and tag-based
technologies, such as microarray, have allowed researchers to obtain intriguing insights into human genetics, even though microarray techniques suffer
from background cross-hybridization issues and a narrow detection range, and tag-based approaches require laborious time- and cost-effective steps
for the cloning of fragments prior sequencing. Recently, the introduction of massively parallel sequencing on Next Generation Sequencing (NGS) platforms
has completely revolutionized the way of thinking in molecular biology.
Among the different application of NGS platforms, RNA-Seq is probably one of the most complex of the various sequencing protocols developed so far.
RNA-Seq has clear advantages over the existing approaches. First, RNA-Seq is not limited to the detection of known transcripts, thus allowing the
identification, characterization and quantification of new splice isoforms. In addition, it permits researchers to determine the correct gene annotation,
also defining the transcriptional boundaries of genes. Other advantages of RNA-Seq are the low "background signal", the absence of an upper limit
for quantification and consequently, the larger dynamic range of expression levels over which transcripts can be detected. RNA-Seq data also show high
levels of reproducibility.
In this seminar we will illustrate some of the computational tools available for the analysis of RNA-Seq data and discuss the main challenges to face
when analyzing RNA-Seq experiments. In particular we will focus on 1) Identification and quantification of transcriptional regions. 2) Identification and
quantification of isoforms. 3) Detection of differential expressed events between two or more experimental conditions. 4) Connection between RNA-seq
and ChIP-seq data. |
22/02/2011 (15.00) [Lieu : Bât. Euler]
Wim MICHIELS (KUL)
Eigenvalue based techniques for the stability analysis and robust control of linear systems with time-delay (slides)
|
| Time-delay systems are a subclass of infinite-dimensional system. They have a variety of applications in engineering,
economics and the bio-sciences. Two mainstream control design approaches for linear time-delay systems can be distinguished in the literature.
The first type is based on applying a generalization of the classical systems and control theory to infinite-dimensional systems.
It mostly results in infinite-dimensional or distributed controllers which may be hard to implement in practical applications where
the controller structure is fixed or restricted, or in controllers that include observers, requiring an on-line numerical simulation
of the systems' equations. The second approach consists of identifying approximate finite-dimensional models of low order, and applying
the existing design methods that typically yield controllers whose dimensions are larger or equal than the dimension of the plant model.
As a drawback the properties of the resulting closed-loop system may heavily depend on the accuracy of the approximation, and the design
involves a trade-off between accuracy and reliability on the one hand and the feasibility of the controller implementation on the other hand.
In my presentation I will give an overview of recent work in my group on control design methods that aim at bridging the gap between the two
types of approaches described above, by designing directly controllers for a broad class of linear time-delay systems (without starting
from a low-order approximation), where the controller structure or order is a-priori specified (e.g. imposed from practical considerations).
These methods are based on a direct optimization of appropriately defined cost functions and inspired by recent work on low-order control
design for finite-dimensional systems within an eigenvalue optimization framework. The analysis and design problems under consideration include
the stabilization problem and the computation and optimization of H2 and H-infinity type cost functions.
Many of the methods discussed heavily rely on the property that eigenvalue problems associated with linear time-delay systems, which
are usually finite-dimensional and nonlinear, can be equivalently expressed as infinite-dimensional linear eigenvalue problems.
I will point out how the underlying linearization approach can be generalized, resulting in generic computational tools for nonlinear eigenvalue
problems. |
15/02/2011 (15.00) [Lieu : Bât. Euler]
Gautier KRINGS (UCL)
The role of second trials in cascades of information over networks (slides)
|
| We study the propagation of information in social networks. To do so, we focus on a cascade model where nodes are infected with
probability p_1 after their first contact with the information and with probability p_2 at all subsequent contacts. The diffusion starts
from one random node and leads to a cascade of infection. It is shown that first and subsequent trials play different roles in the propagation
and that the size of the cascade depends in a nontrivial way on p_1, p_2, and on the network structure. Second trials are shown to amplify
the propagation in dense parts of the network while first trials are dominant for the exploration of new parts of the network and launching
new seeds of infection. |
10/02/2011 (16.30) [Lieu : CYCL01]
Karl SIGMUND (University of Vienna, Austria)
COLLOQUIUM CESAME/MAPA: Public Goods, Free Riders and the Emergence of Sanctions
|
| Punishment of free-riders is generally viewed as an important factor in promoting cooperation. But since it is often costly to sanction
exploiters, the emergence of such a behavior and its stability raise interesting problems. Players who do not contribute to the sanctions, but profit from
the increased level of cooperation caused by them, act as 'second-order exploiters' and threaten the joint enterprise. In this paper, we review the role
of voluntary participation in establishing and upholding cooperation with or without punishment. In particular, we deal with two distinct forms of
punishment, namely peer punishment and pool punishment, and compare their stability and their efficiency. The emergence and upkeep of collaborative
undertakings can strongly depend on whether participation is voluntary or mandatory. The possibility to opt out of a joint enterprise often helps
in curbing exploiters and boosting pro-social behavior. |
1/02/2011 (15.00) [Lieu : Bât. Euler]
Pierre BORCKMANS (UCL)
Derivative-Free Optimization on Matrix Manifolds: Introduction and applications (slides)
|
| Optimization on manifolds is a recent field that is gaining more and more interest. Many applications can naturally be expressed on manifolds,
in order to tackle structure constraints (orthogonality, ...) or invariance properties (rotation, scaling, ...). However, some of these problems may be
non-smooth or non-differentiable, therefore preventing the legit/efficient use of classical optimization algorithms on manifolds (Descent, Newton, ...).
In this talk, we focus on derivative-free optimization on Riemannian manifolds. We briefly present the concept of optimization on manifold, then we
focus on a specific algorithm, namely Particle Swarm Optimization (PSO). We show how PSO can be adapted to matrix manifolds, before applying it
to two practical applications: (1) Oriented Bounding Box Computation (P.B.Borckmans and P.-A. Absil), (2) Low Multilinear-Rank Tensor Approximation
(P.B.Borckmans, M. Isheva and P.-A.Absil). These two problems illustrate the feasibility of the proposed method.
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28/05/2010
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